# Multiply Fractions with Mixed Numbers/Whole Numbers

$\require{cancel}$Multiplying fractions is easy and cross cancelling can be fun. The only tricky part about multiplying fractions is that you can't multiply fractions with mixed numbers. **Mixed numbers must be turned into improper fractions. After you convert to improper fractions, the multiplication process can continue as usual** (for more see lesson Convert Mixed Numbers to Improper Fractions)

*Example*:

$$\eqalign{1\dfrac{1}{7}\times4\dfrac{2}{3}=&\\\dfrac{1\times7+1}{7}\times\dfrac{4\times3+2}{3}=&\quad&&\text{Convert both mixed numbers to improper fractions}\\\dfrac{8}{7}\times\dfrac{14}{3}=&\quad&&\text{Now, you just multiply the fractions}\\\dfrac{8}{\underset{1}{\bcancel{7}}}\times\dfrac{\overset{2}{\bcancel{14}}}{3}=& \quad &&\text{Cross cancel 7 and 14, by dividing each by 7}\\\dfrac{1}{7}\times \dfrac{2}{3}=& \dfrac{2}{21}}$$

Once the numbers are turned into improper fraction, you multiply just like you did in lesson Multiply Fractions (advanced).

Note: Sometimes you have to multiply a fraction by a whole number. The rule (you need a fraction) is the same, but the process is even simpler. Just convert the whole number to a fraction (remember, to make a whole number into a fraction, put a 1 in the denominator) and multiply.

Just to review:

$$\eqalign{1=&\dfrac{1}{1}\\2=&\dfrac{2}{1}\\3=&\dfrac{3}{1}\\4=&\dfrac{4}{1}\\&\text{etc.}}$$

*Example*:

$$\eqalign{\dfrac{1}{9} \times 8=&\\\dfrac{1}{9}\times \dfrac{8}{1}=&\dfrac{8}{9}}$$

Bottom line, to multiply fractions, multiply numerators times numerators and denominators times denominators. But, you can't do this with whole numbers, so convert all whole numbers and mixed numbers into fractions!

#### Practice Problems:

## Fraction Multiplication (With Mixed Numbers)

Find the product. Simplify all answers completely. Change improper fractions to mixed numbers.

1. $6\dfrac{7}{8}$ $\times$ $1\dfrac{5}{11}=$

2. $3\dfrac{1}{2}$ $\times$ $3\dfrac{3}{7}=$

3. $2\dfrac{4}{7}$ $\times$ $4\dfrac{7}{8}=$

4. $3\dfrac{5}{7}$ $\times$ $2\dfrac{1}{5}=$

5. $2\dfrac{2}{3}$ $\times$ $2\dfrac{1}{8}=$

6. $4\dfrac{1}{2}$ $\times$ $3\dfrac{8}{9}=$

7. $3\dfrac{2}{3}$ $\times$ $1\dfrac{2}{22}=$

8. $6\dfrac{1}{8}$ $\times$ $3\dfrac{2}{7}=$

9. $3\dfrac{4}{7}$ $\times$ $2\dfrac{1}{3}=$

10. $2\dfrac{5}{8}$ $\times$ $1\dfrac{1}{7}=$

11. $1\dfrac{1}{64}$ $\times$ $6\dfrac{2}{5}=$

12. $1\dfrac{6}{9}$ $\times$ $3\dfrac{2}{3}=$

#### Answer Key: